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IEN311D1 Project1

# IEN311D1 Project1 - Yue Xu IEN311 D1 Project1 Part 1...

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Yue Xu IEN311 D1 Project1 Part 1 Generating Discrete Random Numbers (i) Binomial (10,0.1) Random Numbers Binomial (10,0.1) mean var n=100 1.0900 1.0322 n=1000 0.9950 0.8759 n=10000 0.9991 0.9011

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n=X 1 1 Summarize As the sample size n → ∞, the shape of the histogram converges to the shape of the PMF of the binomial distribution. As the sample size n → ∞, the expectation and variance converges to the expectation and variance of the binomial distribution. (ii) Poisson (5) Random Numbers Poisson (5) mean var
n=100 5.2800 5.1127 n=1000 4.9770 4.9334 n=10000 5.0029 4.9874 n=X 5 5 Summarize As the sample size n → ∞, the shape of the histogram converges to the shape of the PMF of the Poisson distribution. As the sample size n → ∞, the expectation and variance converges to the expectation and variance of the Poisson distribution. (iii) Relationships between Binomial and Poisson

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XX=binornd(10,0.5,1,10000) XX=binornd(100,0.05,1,10000) XX=binornd(1000,0.005,1,10000) XX=binornd(10000,0.0005,1,10000) XX=poissrnd(5,1,10000) Summarize As the number of sample take → ∞, the shape of the histogram of Binomial distribution converges to the shape of the histogram of the Poisson distribution.
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